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Bottom panel: mass density distribution obtained with ADER-Cons.
Top panel: mass density distribution obtained with ADER-Prim.
It is assumed that mass density distribution in the medium follows a power law of the radial distance from the point of explosion.
The solution to the tails problem can only derive from abandoning completely the probabilistic interpretation and from adopting a more physical and realistic interpretation relating 'what is out there' to, e.g., the mass density distribution over the whole universe.
Adding a correction calculated from the empirical relation to the NRLMSISE-00 model reference leads to a better prediction of storm-time thermospheric mass density distribution.
The difference between the converged 1D solution and the relaxed 2D solutions with (N_{r}=800) (dotted lines) and (N_{r}=1600) (dashed lines) is illustrated in Figure 6 which shows the mass density distribution.
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Figure 22 shows the rest-mass density distribution on the ((x,y)) plane for this test.
Two-dimensional rest-mass density distribution relative to the initial data maximum value on the equatorial ((x,y)) plane for the grazing-collision tests at time (t=768~M_{odot}), i.e., after the point of closest approach.
In Figure 17 we show the rest-mass density distribution on the equatorial plane for both schemes and during one of the contractions of the star, just before the central rest-mass density reaches a maximum (cf., Figure 18).
Two-dimensional rest-mass density distribution relative to the initial data maximum value on the equatorial ((x,y)) plane at time (t=1text167~M_{odot}) for the migration test.
In Figure 20 we report again the rest-mass density distribution on the equatorial plane for both schemes and at time (t=4text300~M_{odot}), that is, after about 14 rotation periods.
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